Reduced Donaldson–Thomas multiple-cover conjecture for abelian threefolds

Let $A$ be an abelian threefold, and let $\beta\in H_2(A,\mathbb Z)$ be a curve class of type $(d_1,d_2,d_3)$. Write $\mathsf{DT}^{\mathrm{red}}_{n,(d_1,d_2,d_3)}$ for the reduced Donaldson–Thomas invariant. Define $\mathsf{a}(k)$ by the coefficients of $-\phi_{-2,1}(p,t)$, and let $\mathsf{n}(d_1,d_2,d_3,k)$ be the sum of $\delta^2$ over the divisors $\delta$ of the displayed greatest common divisor when all its entries are integers. The abelian threefold multiple-cover conjecture. If $n>0$ or at least two of the $d_i$ are positive, then

$$(-1)^n\mathsf{DT}^{\mathrm{red}}_{n,(d_1,d_2,d_3)}=\sum_k\frac{1}{k}\,\mathsf{n}(d_1,d_2,d_3,k)\,\mathsf{a}\left(\frac{4d_1d_2d_3-n^2}{k^2}\right),$$

where $k$ runs over all divisors of $\gcd(n,d_1d_2,d_1d_3,d_2d_3)$ such that $k^2\mid d_1d_2d_3$. This is the proposed multiple-cover formula for reduced Donaldson–Thomas invariants of abelian threefolds; the source does not specify its resolution status.